The Padé iterations for the matrix sign function and their reciprocals are optimal
Copyright policy )The Padé iterations for the matrix sign function and their reciprocals are optimal
It is proved that among the rational iterations locally converging with order s>1 to the sign function, the Padé iterations and their reciprocals are the unique rationals with the lowest sum of the degrees of numerator and denominator.
- University of Pisa Italy
- University of Perugia Italy
- Scuola Normale Superiore Italy
Rational iterations; Matrix functions; Matrix sign function; Local convergence; Padé approximation; Root-finding algorithm, Matrix sign function, computational efficiency, Halley's method, Horner's scheme, matrix functions, General theory of numerical methods in complex analysis (potential theory, etc.), Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral), FOS: Mathematics, Discrete Mathematics and Combinatorics, Mathematics - Numerical Analysis, Local convergence, Padé approximation, Numerical Analysis, Algebra and Number Theory, Rational iterations, Other matrix algorithms, matrix sign function, Matrix functions, root-finding algorithm, Numerical Analysis (math.NA), Newton's method, Root-finding algorithm, Numerical computation of roots of polynomial equations, rational iterations, local convergence, Geometry and Topology, Newton-Schulz iteration
Rational iterations; Matrix functions; Matrix sign function; Local convergence; Padé approximation; Root-finding algorithm, Matrix sign function, computational efficiency, Halley's method, Horner's scheme, matrix functions, General theory of numerical methods in complex analysis (potential theory, etc.), Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral), FOS: Mathematics, Discrete Mathematics and Combinatorics, Mathematics - Numerical Analysis, Local convergence, Padé approximation, Numerical Analysis, Algebra and Number Theory, Rational iterations, Other matrix algorithms, matrix sign function, Matrix functions, root-finding algorithm, Numerical Analysis (math.NA), Newton's method, Root-finding algorithm, Numerical computation of roots of polynomial equations, rational iterations, local convergence, Geometry and Topology, Newton-Schulz iteration
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